An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices

We show that for every p s (1, ∞) there exists a weight w such that the Lorentz Gamma space Γp,w is reflexive, its lower Boyd and Zippin indices are equal to zero and its upper Boyd and Zippin indices are equal to one. As a consequence, the Hardy-Littlewood maximal operator is unbounded on the constructed reflexive space Γp,w and on its associate space $$\Gamma _{p,w}^\prime$$ .